فهرست نشریات علمی دسترسی آزاد ایران

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎The purpose of this paper is to introduce and investigate the submodules of an $R$-module $M$ which satisfy the dual of Property $\mathcal{A}$‎, ‎the dual of strong Property $\mathcal{A}$‎, ‎and the dual of proper strong Property $\mathcal{A}$‎. ‎Moreover‎, ‎a submodule $N$ of $M$ which satisfy Property $\mathcal{S_J(N)}$ and Property $\mathcal{I^M_J(N)}$ will be introduced and investigated‎.